Metric Lie n-algebras and double extensions

Details Metric Lie n-algebras and double extensions Metric Lie n-algebras and double extensions

2008-06-21

arxiv.org/abs/0806.3534v1

Mathematics

Representation Theory

10 pages

Scientific paper

We prove a structure theorem for Lie n-algebras possessing an invariant inner
product. We define the notion of a double extension of a metric Lie n-algebra
by another Lie n-algebra and prove that all metric Lie n-algebras are obtained
from the simple and one-dimensional ones by iterating the operations of
orthogonal direct sum and double extension.

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